The MI Procedure
- Overview
- Getting Started
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Syntax
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DetailsDescriptive StatisticsEM Algorithm for Data with Missing ValuesStatistical Assumptions for Multiple ImputationMissing Data PatternsImputation MethodsMonotone Methods for Data Sets with Monotone Missing PatternsMonotone and FCS Regression MethodsMonotone and FCS Predictive Mean Matching MethodsMonotone and FCS Discriminant Function MethodsMonotone and FCS Logistic Regression MethodsMonotone Propensity Score MethodFCS Methods for Data Sets with Arbitrary Missing PatternsChecking Convergence in FCS MethodsMCMC Method for Arbitrary Missing Multivariate Normal DataProducing Monotone Missingness with the MCMC MethodMCMC Method SpecificationsChecking Convergence in MCMCInput Data SetsOutput Data SetsCombining Inferences from Multiply Imputed Data SetsMultiple Imputation EfficiencyImputer’s Model Versus Analyst’s ModelParameter Simulation versus Multiple ImputationSensitivity Analysis for the MAR AssumptionMultiple Imputation with Pattern-Mixture ModelsSpecifying Sets of Observations for Imputation in Pattern-Mixture ModelsAdjusting Imputed Values in Pattern-Mixture ModelsSummary of Issues in Multiple ImputationODS Table NamesODS Graphics
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ExamplesEM Algorithm for MLEMonotone Propensity Score MethodMonotone Regression MethodMonotone Logistic Regression Method for CLASS VariablesMonotone Discriminant Function Method for CLASS VariablesFCS Method for Continuous VariablesFCS Method for CLASS VariablesFCS Method with Trace PlotMCMC MethodProducing Monotone Missingness with MCMCChecking Convergence in MCMCSaving and Using Parameters for MCMCTransforming to NormalityMultistage ImputationCreating Control-Based Pattern Imputation in Sensitivity AnalysisAdjusting Imputed Continuous Values in Sensitivity AnalysisAdjusting Imputed Classification Levels in Sensitivity AnalysisAdjusting Imputed Values with Parameters in a Data Set
- References
- 63.1 EM Algorithm for MLE
- 63.2 Monotone Propensity Score Method
- 63.3 Monotone Regression Method
- 63.4 Monotone Logistic Regression Method for CLASS Variables
- 63.5 Monotone Discriminant Function Method for CLASS Variables
- 63.6 FCS Method for Continuous Variables
- 63.7 FCS Method for CLASS Variables
- 63.8 FCS Method with Trace Plot
- 63.9 MCMC Method
- 63.10 Producing Monotone Missingness with MCMC
- 63.11 Checking Convergence in MCMC
- 63.12 Saving and Using Parameters for MCMC
- 63.13 Transforming to Normality
- 63.14 Multistage Imputation
- 63.15 Creating Control-Based Pattern Imputation in Sensitivity Analysis
- 63.16 Adjusting Imputed Continuous Values in Sensitivity Analysis
- 63.17 Adjusting Imputed Classification Levels in Sensitivity Analysis
- 63.18 Adjusting Imputed Values with Parameters in a Data Set
The Fish data described in the STEPDISC procedure are measurements of 159 fish of seven species caught in Finland’s Lake Laengelmaevesi.
For each fish, the length, height, and width are measured. Three different length measurements are recorded: from the nose
of the fish to the beginning of its tail (Length1), from the nose to the notch of its tail (Length2), and from the nose to the end of its tail (Length3). See Chapter 96: The STEPDISC Procedure, for more information.
The Fish1 data set is constructed from the Fish data set and contains only one species of the fish and the three length measurements. Some values have been set to missing,
and the resulting data set has a monotone missing pattern in the variables Length1, Length2, and Length3. The Fish1 data set is used in Example 63.2 with the propensity score method and in Example 63.3 with the regression method.
The Fish2 data set is also constructed from the Fish data set and contains two species of fish. Some values have been set to missing, and the resulting data set has a monotone
missing pattern in the variables Length, Width, and Species. The Fish2 data set is used in Example 63.4 with the logistic regression method and in Example 63.5 with the discriminant function method. Note that some values of the variable Species have also been altered in the data set.
The Fish3 data set is similar to the data set Fish2 except some additional values have been set to missing and the resulting data set has an arbitrary missing pattern. The Fish3 data set is used in Example 63.7 and in Example 63.8.
The Fitness1 data set created in the section Getting Started: MI Procedure is used in other examples.
The following statements create the Fish1 data set:
*-----------------------------Fish1 Data-----------------------------* | The data set contains one species of the fish (Bream) and | | three measurements: Length1, Length2, Length3. | | Some values have been set to missing, and the resulting data set | | has a monotone missing pattern in the variables | | Length1, Length2, and Length3. | *--------------------------------------------------------------------*; data Fish1; title 'Fish Measurement Data'; input Length1 Length2 Length3 @@; datalines; 23.2 25.4 30.0 24.0 26.3 31.2 23.9 26.5 31.1 26.3 29.0 33.5 26.5 29.0 . 26.8 29.7 34.7 26.8 . . 27.6 30.0 35.0 27.6 30.0 35.1 28.5 30.7 36.2 28.4 31.0 36.2 28.7 . . 29.1 31.5 . 29.5 32.0 37.3 29.4 32.0 37.2 29.4 32.0 37.2 30.4 33.0 38.3 30.4 33.0 38.5 30.9 33.5 38.6 31.0 33.5 38.7 31.3 34.0 39.5 31.4 34.0 39.2 31.5 34.5 . 31.8 35.0 40.6 31.9 35.0 40.5 31.8 35.0 40.9 32.0 35.0 40.6 32.7 36.0 41.5 32.8 36.0 41.6 33.5 37.0 42.6 35.0 38.5 44.1 35.0 38.5 44.0 36.2 39.5 45.3 37.4 41.0 45.9 38.0 41.0 46.5 ;
The Fish2 data set contains two of the seven species in the Fish data set. For each of the two species (Bream and Pike), the length from the nose of the fish to the end of its tail and the width of each fish are measured.
The following statements create the Fish2 data set:
*-----------------------------Fish2 Data-----------------------------* | The data set contains two species of the fish (Parkki and Perch) | | and two measurements: Length and Width. | | Some values have been set to missing, and the resulting data set | | has a monotone missing pattern in the variables | | Length, Width, and Species. | *--------------------------------------------------------------------*; data Fish2; title 'Fish Measurement Data'; input Species $ Length Width @@; datalines; Parkki 16.5 2.3265 Parkki 17.4 2.3142 . 19.8 . Parkki 21.3 2.9181 Parkki 22.4 3.2928 . 23.2 3.2944 Parkki 23.2 3.4104 Parkki 24.1 3.1571 . 25.8 3.6636 Parkki 28.0 4.1440 Parkki 29.0 4.2340 Perch 8.8 1.4080 . 14.7 1.9992 Perch 16.0 2.4320 Perch 17.2 2.6316 Perch 18.5 2.9415 Perch 19.2 3.3216 . 19.4 . Perch 20.2 3.0502 Perch 20.8 3.0368 Perch 21.0 2.7720 Perch 22.5 3.5550 Perch 22.5 3.3075 . 22.5 . Perch 22.8 3.5340 . 23.5 . Perch 23.5 3.5250 Perch 23.5 3.5250 Perch 23.5 3.5250 Perch 23.5 3.9950 . 24.0 . Perch 24.0 3.6240 Perch 24.2 3.6300 Perch 24.5 3.6260 Perch 25.0 3.7250 . 25.5 3.7230 Perch 25.5 3.8250 Perch 26.2 4.1658 Perch 26.5 3.6835 . 27.0 4.2390 Perch 28.0 4.1440 Perch 28.7 5.1373 . 28.9 4.3350 . 28.9 . . 28.9 4.5662 Perch 29.4 4.2042 Perch 30.1 4.6354 Perch 31.6 4.7716 Perch 34.0 6.0180 . 36.5 6.3875 . 37.3 7.7957 . 39.0 . . 38.3 . Perch 39.4 6.2646 Perch 39.3 6.3666 Perch 41.4 7.4934 Perch 41.4 6.0030 Perch 41.3 7.3514 . 42.3 . Perch 42.5 7.2250 Perch 42.4 7.4624 Perch 42.5 6.6300 Perch 44.6 6.8684 Perch 45.2 7.2772 Perch 45.5 7.4165 Perch 46.0 8.1420 Perch 46.6 7.5958 ;
The following statements create the Fish3 data set:
*-----------------------------Fish3 Data-----------------------------* | The data set contains three species of the fish | | (Parkki, Perch, and Roach) and two measurements: Length and Width. | | Some values have been set to missing, and the resulting data set | | has an arbitrary missing pattern in the variables | | Length, Width, and Species. | *--------------------------------------------------------------------*; data Fish3; title 'Fish Measurement Data'; input Species $ Length Width @@; datalines; Roach 16.2 2.2680 Roach 20.3 2.8217 Roach 21.2 . Roach . 3.1746 Roach 22.2 3.5742 Roach 22.8 3.3516 Roach 23.1 3.3957 . 23.7 . Roach 24.7 3.7544 Roach 24.3 3.5478 Roach 25.3 . Roach 25.0 3.3250 Roach 25.0 3.8000 Roach 27.2 3.8352 Roach 26.7 3.6312 Roach 26.8 4.1272 Roach 27.9 3.9060 Roach 29.2 4.4968 Roach 30.6 4.7736 Roach 35.0 5.3550 Parkki 16.5 2.3265 Parkki 17.4 . Parkki 19.8 2.6730 Parkki 21.3 2.9181 Parkki 22.4 3.2928 Parkki 23.2 3.2944 Parkki 23.2 3.4104 Parkki 24.1 3.1571 . . 3.6636 Parkki 28.0 4.1440 Parkki 29.0 4.2340 Perch 8.8 1.4080 . 14.7 1.9992 Perch 16.0 2.4320 Perch 17.2 2.6316 Perch 18.5 2.9415 Perch 19.2 3.3216 . 19.4 3.1234 Perch 20.2 . Perch 20.8 3.0368 Perch 21.0 2.7720 Perch 22.5 3.5550 Perch 22.5 3.3075 Perch 22.5 3.6675 Perch . 3.5340 Perch 23.5 3.4075 Perch 23.5 3.5250 Perch 23.5 3.5250 . 23.5 3.5250 Perch 23.5 3.9950 Perch 24.0 3.6240 Perch 24.0 3.6240 Perch 24.2 3.6300 Perch 24.5 3.6260 Perch 25.0 3.7250 Perch . 3.7230 Perch 25.5 3.8250 Perch . 4.1658 Perch 26.5 3.6835 . 27.0 4.2390 Perch . 4.1440 Perch 28.7 5.1373 . 28.9 4.3350 Perch 28.9 4.3350 Perch 28.9 4.5662 Perch 29.4 4.2042 Perch 30.1 4.6354 Perch 31.6 4.7716 Perch 34.0 6.0180 Perch 36.5 6.3875 Perch 37.3 7.7957 Perch 39.0 . Perch 38.3 6.7408 Perch . 6.2646 . 39.3 . Perch 41.4 7.4934 Perch 41.4 6.0030 Perch 41.3 7.3514 Perch 42.3 7.1064 Perch 42.5 7.2250 Perch 42.4 7.4624 Perch 42.5 6.6300 Perch 44.6 6.8684 Perch 45.2 7.2772 Perch 45.5 7.4165 Perch 46.0 8.1420 . 46.6 7.5958 ;